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Matching and Edge Cover in Temporal Graphs

Authors Lapo Cioni , Riccardo Dondi , Andrea Marino , Jason Schoeters , Ana Silva

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Matchings and factors
  • Mathematics of computing → Approximation algorithms
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Fixed parameter tractability
Keywords
  • graphs
  • temporal graphs
  • edge cover
  • matching
  • parameterized algorithm
  • approximation algorithm

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Abstract

Temporal graphs are a special class of graphs for which a temporal component is added to edges, that is, each edge possesses a set of times at which it is available and can be traversed. Many classical problems on graphs can be translated to temporal graphs, and the results may differ.
In this paper, we define the {Temporal Edge Cover} and {Temporal Matching} problems and show that they are NP-complete even when fixing the lifetime or when the underlying graph is a tree. We then describe two FPT algorithms, with parameters lifetime and treewidth, that solve the two problems. We also find lower bounds for the approximation of the two problems and give two approximation algorithms which match these bounds. Finally, we discuss the differences between the problems in the temporal and the static framework.

Cite As Get BibTex

Lapo Cioni, Riccardo Dondi, Andrea Marino, Jason Schoeters, and Ana Silva. Matching and Edge Cover in Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SAND.2025.8

Author Details

Lapo Cioni
  • Università degli Studi di Firenze, Italy
Riccardo Dondi
  • Università degli Studi di Bergamo, Italy
Andrea Marino
  • Università degli Studi di Firenze, Italy
Jason Schoeters
  • Università degli Studi di Firenze, Italy
Ana Silva
  • Universidade Federal do Ceará, Fortaleza, Brasil

Funding

This paper was partially funded by Italian PNRR CN4 Centro Nazionale per la Mobilità Sostenibile, NextGeneration EU - CUP, B13C22001000001. MUR of Italy, under PRIN Project n. 2022ME9Z78 - NextGRAAL: Next-generation algorithms for constrained GRAph visuALization, PRIN PNRR Project n. P2022NZPJA - DLT-FRUIT: A user centered framework for facilitating DLTs FRUITion.

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